A lag switch is a device installed on a home network that temporarily slows down the flow of traffic to the internet. In an online gaming context, the physical switch can be turned on to slow down gameplay and give the lag switcher the upper hand.
LAG (LAGG) is a good thing!
An example that indicates a lag switch is in use is if the opponent jumps around on the screen when you shoot the character. Or maybe the character appears invisible and completely unharmed by close range shots.
When a lag switch is activated, it operates on a short timer that usually lasts a few seconds. During this time, it effectively blocks all network traffic between the game console and the internet.
Because the game recognizes that the user's internet is down, the player appears paused and unresponsive. However, the game does not kick the user out because it assumes that the connection will be resumed shortly. During this time, the user can still play locally.